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Proofs with Matricies

  1. Sep 15, 2012 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations

    Question 1.jpg


    3. The attempt at a solution

    -(y, x) = -(YX-XY)
    = XY-YX

    Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)

    And prove it that way? I am just really confused
     
  2. jcsd
  3. Sep 15, 2012 #2

    Mark44

    Staff: Mentor

    What you have above would work, but your notation is awful! Try to use the notation as given in the problem. Also notice that uppercase letters represent matrices, and lowercase letters represent the entries in a matrix.

    Assuming that matrices X and Y are in M, then [X, Y] = ?
    Keep working with the expressions you get until you end up with -[Y, X].
     
  4. Sep 15, 2012 #3
    [X, Y]= YX- XY
    Thus [Y, X]= XY- YX
    then -[Y, X]= -(XY- YX)
    then -[Y, X]= -XY +YX

    Like that? So i don't have to use matricies with variables, just use X and Y to represent a matrix?
     
  5. Sep 15, 2012 #4

    Mark44

    Staff: Mentor

    This is easier to follow.

    [X, Y] = XY - YX = -(YX - XY) = -[Y, X]

    Can you say why each pair of successive equal expressions is valid?
     
  6. Sep 15, 2012 #5
    Properties of Matricies?
     
  7. Sep 15, 2012 #6
    And Thanks your honestly a huge help!
     
  8. Sep 16, 2012 #7

    Mark44

    Staff: Mentor

    That's pretty vague. Also, there are a number of steps. One reason doesn't fit them all.
     
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